## Time Series Forecasting with ARIMA

This tutorial demonstrates how to implement the models and forecasting discussed in this unit. Since we are using Google Colab, you can jump to Step 2 to begin this programming example. Upon completing this tutorial, you should be able to construct models, make forecasts and validate forecasts given a time series data set.

### Step 7 - Producing and Visualizing Forecasts

In the final step of this tutorial, we describe how to leverage our
seasonal ARIMA time series model to forecast future values. The `get_forecast()`

attribute of our time series object can compute forecasted values for a specified number of steps ahead.

# Get forecast 500 steps ahead in future pred_uc = results.get_forecast(steps=500) # Get confidence intervals of forecasts pred_ci = pred_uc.conf_int()

We can use the output of this code to plot the time series and forecasts of its future values.

ax = y.plot(label='observed', figsize=(20, 15)) pred_uc.predicted_mean.plot(ax=ax, label='Forecast') ax.fill_between(pred_ci.index, pred_ci.iloc[:, 0], pred_ci.iloc[:, 1], color='k', alpha=.25) ax.set_xlabel('Date') ax.set_ylabel('CO2 Levels') plt.legend() plt.show()

Both the forecasts and associated confidence interval that we have generated can now be used to further understand the time series and foresee what to expect. Our forecasts show that the time series is expected to continue increasing at a steady pace.

As we forecast further out into the future, it is natural for us to become less confident in our values. This is reflected by the confidence intervals generated by our model, which grow larger as we move further out into the future.